{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## load pacakges\n",
    "push!(LOAD_PATH, pwd()) # add the current folder, which contains Utils.jl, to LOAD_PATH\n",
    "using Utils, DataFrames, PyPlot, NLsolve, Optim, Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## matplotlib settings\n",
    "#  not important, only to write latex on graphs\n",
    "fontsize = 16; fonttype = \"serif\"\n",
    "# fonttype = \"sansserif\"\n",
    "PyPlot.matplotlib.rc(\"text\", usetex=true) # allow tex rendering\n",
    "PyPlot.matplotlib.rcParams[\"text.latex.unicode\"] = true\n",
    "if fonttype==\"serif\" # use serif math font\n",
    "    PyPlot.matplotlib.rc(\"font\", family=\"serif\", serif=\"Times\", size=16)\n",
    "    #PyPlot.matplotlib.rc(\"text.latex\",preamble=\"\\\\usepackage[libertine]{newtxmath}\")\n",
    "else # use sans serif math font\n",
    "    PyPlot.matplotlib.rc(\"font\", family=\"sans-serif\", size=16)\n",
    "    PyPlot.matplotlib.rc(\"text.latex\",preamble=\"\\\\usepackage{newtxsf}\")\n",
    "end\n",
    "PyPlot.matplotlib.rcParams[\"text.latex.unicode\"] = false;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions to solve equilibrium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "solveDemographics (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## solve for μ given mm and ss for a market\n",
    "function solveDemographics(para)\n",
    "    ρ, n, λu, λd, md, s = para\n",
    "    η = λu/(λu + λd)\n",
    "    function resolveDemographicsX(x)\n",
    "        di = Dict()\n",
    "        di[:mDO] = transBetween(x[1],lower=0.0,upper=md)\n",
    "        di[:mDN] = md - di[:mDO]\n",
    "        di[:νLO] = 1.0 - (1.0 - di[:mDN]/md)^n\n",
    "        di[:νHN] = 1.0 - (1.0 - di[:mDO]/md)^n\n",
    "        di[:mHO] = η*di[:νHN]*(λu + di[:νLO]*ρ)/(λu*di[:νHN] + λd*di[:νLO] + di[:νLO]*di[:νHN]*ρ)\n",
    "        di[:mHN] = η - di[:mHO]\n",
    "        di[:mLO] = (1.0 - η)*(λu*di[:νHN])/(λu*di[:νHN] + λd*di[:νLO] + di[:νLO]*di[:νHN]*ρ)\n",
    "        di[:mLN] = (1.0 - η) - di[:mLO]\n",
    "        return di\n",
    "    end\n",
    "    function f!(fvec,x)\n",
    "        di = resolveDemographicsX(x)\n",
    "        fvec[1] = di[:mHO] + di[:mLO] + di[:mDO] - s\n",
    "    end\n",
    "    sol = nlsolve(f!,rand(1))#,method=:newton)\n",
    "    converging = sol.x_converged | sol.f_converged\n",
    "    return converging, resolveDemographicsX(sol.zero)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "solveValueFunctions (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## solve for value functions given demographics for a market\n",
    "function solveValueFunctions(para,di0;ABBar=nothing)\n",
    "    ρ, n, λu, λd, yh, yd, yl, r, fc, fd, qLO, qHN, mc, md, s = para\n",
    "    rc = r + fc; rd = r + fd # combine discount rate with death rate\n",
    "    di = deepcopy(di0)\n",
    "    ## trading gain intensities\n",
    "    if isnothing(ABBar)\n",
    "        di[:ABar] = n*di[:mDO]/md*(1.0 - di[:mDO]/md)^(n-1)/(1.0 - (1.0 - di[:mDO]/md)^n)\n",
    "        di[:BBar] = n*di[:mDN]/md*(1.0 - di[:mDN]/md)^(n-1)/(1.0 - (1.0 - di[:mDN]/md)^n)\n",
    "    else\n",
    "        di[:ABar], di[:BBar] = ABBar\n",
    "    end\n",
    "    di[:γLO] = qLO + (1.0 - qLO)*(1.0 - di[:BBar])\n",
    "    di[:γHN] = qHN + (1.0 - qHN)*(1.0 - di[:ABar])\n",
    "    di[:ζLO] = ρ*di[:νLO]*di[:γLO]\n",
    "    di[:ζHN] = ρ*di[:νHN]*di[:γHN]\n",
    "    di[:ζDO] = di[:mHN]*ρ*di[:νHN]/di[:mDO]*(1.0 - di[:γHN])\n",
    "    di[:ζDN] = di[:mLO]*ρ*di[:νLO]/di[:mDN]*(1.0 - di[:γLO])\n",
    "    ## value functions\n",
    "    ΔDenominator = rc^2*(rd + di[:ζDN] + di[:ζDO]) + rd*di[:ζLO]*(di[:ζHN] + λd) + rd*di[:ζHN]*λu + rc*(di[:ζDN]*(di[:ζHN] + λd + λu) + di[:ζDO]*(di[:ζLO] + λd + λu) + rd*(di[:ζHN] + di[:ζLO] + λd + λu))\n",
    "    di[:ΔHD] = maximum([0.0, yl*(-rc*di[:ζDN] + rd*λd) + yh*(rc*rd + rc*di[:ζDN] + rd*(di[:ζLO] + λu)) - yd*(rc^2 + rc*(di[:ζLO] + λd + λu))])/ΔDenominator\n",
    "    di[:ΔDL] = maximum([0.0, -yl*(rc*di[:ζDO] + rc*rd + rd*(di[:ζHN] + λd)) + yh*(rc*di[:ζDO] - rd*λu) + yd*(rc^2 + rc*(di[:ζHN] + λd + λu))])/ΔDenominator\n",
    "    vDenominator = rc*(rc + λd + λu)\n",
    "    di[:Rd]  = (yd + di[:ζDO]*di[:ΔHD] - di[:ζDN]*di[:ΔDL])/rd\n",
    "    di[:Rl]  = ((rc + λd)*yl + λu*yh + (rc + λd)*di[:ζLO]*di[:ΔDL] - λu*di[:ζHN]*di[:ΔHD])/vDenominator\n",
    "    di[:Rh]  = (λd*yl + (rc + λu)*yh + λd*di[:ζLO]*di[:ΔDL] - (rc + λu)*di[:ζHN]*di[:ΔHD])/vDenominator\n",
    "    di[:vHO] = ((yl + di[:ΔDL]*di[:ζLO])*λd + yh*(rc + λu))/vDenominator\n",
    "    di[:vLN] = di[:ΔHD]*di[:ζHN]*λu/vDenominator\n",
    "    di[:vHN] = di[:ΔHD]*di[:ζHN]*(rc + λu)/vDenominator\n",
    "    di[:vLO] = ((yl + di[:ΔDL]*di[:ζLO])*(rc + λd) + yh*λu)/vDenominator\n",
    "    di[:vDO] = (yd + di[:ΔHD]*di[:ζDO])/rd\n",
    "    di[:vDN] = di[:ΔDL]*di[:ζDN]/rd\n",
    "    ## welfare\n",
    "    di[:welfare] = (yh*di[:mHO] + yd*di[:mDO] + yl*di[:mLO])/r \n",
    "    ## return\n",
    "    return di\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table1: Calibration of the deomographic parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "### data\n",
    "diData=Dict(\n",
    "#     :ρ => free parameter, ranging from 1 to 1000\n",
    "    :n => 27, # HM15 Table VI, Odd lot, most common per Fig 2 of  O'Hara and Zhou (2021)\n",
    "    :md => 0.10, # MarketAxess press release\n",
    "    :turnover => 0.585, # = 0.78*0.75 from Bessembinder et al. (2018), with 25% inter-dealer volume\n",
    "    :tradeCount => 63.4426, # = 467,614/5,528/(4/3) a year\n",
    "    :s => 0.1205, # tradeCount/900 = 2t = turnover*s\n",
    "    :noResponse => 0.086, # HM15 Table VI, Odd lot, most common per Fig 2 of  O'Hara and Zhou (2021)\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "calibrateηλ (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### function to solve for η and λ\n",
    "function calibrateηλ(para,moments;summary=false,guess=nothing)\n",
    "    ρ, n, md = para\n",
    "    s = moments[:s] # take as given\n",
    "    ## resolve X\n",
    "    function resolveX(x)\n",
    "        η = transBetween(x[1],lower=0.0,upper=1.0)\n",
    "        λ = transBetween(x[2],lower=0.0,upper=Inf)\n",
    "        return η, λ\n",
    "    end\n",
    "    ## objective function\n",
    "    function obj(x)\n",
    "        η, λ = resolveX(x)\n",
    "        cvg, di = solveDemographics([ρ,n,λ*η,λ*(1.0-η),md,s,])\n",
    "        obj1 = (moments[:noResponse] - (1.0 - (di[:mHN]*di[:νHN] + di[:mLO]*di[:νLO])/(di[:mHN] + di[:mLO])))^2*1e4\n",
    "        obj2 = (moments[:turnover] - (ρ*di[:mLO]*di[:νLO] + ρ*di[:mHN]*di[:νHN])/s)^2*1e4\n",
    "        return obj1, obj2#, obj3\n",
    "    end\n",
    "    ## do optimization\n",
    "    if isnothing(guess)\n",
    "        guess = rand(2)\n",
    "    else\n",
    "        guess = [\n",
    "            transBetween(guess[1],lower=0.0,upper=1.0,reverse=true),\n",
    "            transBetween(guess[2],lower=0.0,upper=Inf,reverse=true),\n",
    "        ]\n",
    "    end\n",
    "    out = Optim.optimize(x->sum(obj(x)), guess)#, LBFGS())\n",
    "    cvg = Optim.converged(out)\n",
    "    η, λ = resolveX(Optim.minimizer(out))\n",
    "    fmin = obj(Optim.minimizer(out))\n",
    "    if summary\n",
    "        display(Optim.summary(out))\n",
    "    end\n",
    "    return cvg, sqrt.(fmin), η, λ\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×4 Matrix{Any}:\n",
       "     \"converged?\"   \"η\"       \"λ\"       \"s\"\n",
       " true              0.113969  0.350469  0.1205"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### estimate η and λ as reported in Table 1\n",
    "let\n",
    "    di = diData\n",
    "    ρ = 100.0\n",
    "    cvg, fmin, η, λ = calibrateηλ([ρ,di[:n],0.1,], di,)\n",
    "    display([\"converged?\" \"η\" \"λ\" \"s\"; cvg η λ di[:s]])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 8 and 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "### calculate equilibrium\n",
    "\n",
    "## set data\n",
    "di = diData\n",
    "\n",
    "## exogenously fixed parameters\n",
    "md0 = 0.1\n",
    "r0 = 0.05; fc0 = 0.0; fd0 = 0.0\n",
    "yl0 = 0.2; yd0 = NaN; yh0 = 1.0 # yd will be updated\n",
    "\n",
    "## lambda and yd ranges\n",
    "ρRange = exp.(range(log(1e0),stop=log(1e3),length=1000))\n",
    "ydRange = range(0.2,stop=1.1,length=100)\n",
    "\n",
    "## which parameters to store\n",
    "liVrb = [:mLO, :welfare,]\n",
    "\n",
    "## initialize storage\n",
    "diOut1 = Dict(); diOut2 = Dict()\n",
    "for pr in [liVrb; :inbound;]\n",
    "    diOut1[pr] = Array{Float64}(undef, length(ρRange), length(ydRange))\n",
    "    diOut2[pr] = Array{Float64}(undef, length(ρRange), length(ydRange))\n",
    "end\n",
    "\n",
    "## compute\n",
    "guess = [0.12,0.5] # η, λ\n",
    "for (rr,ρ) in enumerate(ρRange)\n",
    "    s = di[:s] # get s directly from data\n",
    "    ## first calibrate η and λ\n",
    "    η, λ = NaN, NaN # must be initialized before try and catch\n",
    "    cvg = false\n",
    "    try\n",
    "        cvg, fmin, η, λ = calibrateηλ([ρ,di[:n],md0,], di, guess=guess)\n",
    "        if cvg # update the guess\n",
    "            guess = [η, λ,]\n",
    "        end\n",
    "    catch e\n",
    "        println(e)\n",
    "    end\n",
    "    for (cc,yd) in enumerate(ydRange)\n",
    "        if cvg\n",
    "            para = [ρ, di[:n], λ*η, λ*(1-η), yh0, yd, yl0, r0, fc0, fd0, 0.0, 0.0, 1.0, md0, s]\n",
    "            ## Scenario 1\n",
    "            cvg1, di1 = solveDemographics([ρ,para[2],λ*η,λ*(1-η),md0,s])\n",
    "            di1 = solveValueFunctions(para,di1)\n",
    "            ## Scenario 2\n",
    "            para[2] += 1 # increase n by 1\n",
    "            cvg2, di2 = solveDemographics([ρ,para[2],λ*η,λ*(1-η),md0,s])\n",
    "            di2 = solveValueFunctions(para,di2)\n",
    "            ## update η, ρ, s\n",
    "            di1[:s] = di2[:s] = s; di1[:η] = di2[:η] = η; di1[:ρ] = di2[:ρ] = ρ; di1[:λ] = di2[:λ] = λ\n",
    "        end\n",
    "        ## save\n",
    "        for pr in liVrb\n",
    "            if cvg\n",
    "                diOut1[pr][rr,cc] = (cvg1 ? di1[pr] : NaN)\n",
    "                diOut2[pr][rr,cc] = (cvg2 ? di2[pr] : NaN)\n",
    "            else\n",
    "                diOut1[pr][rr,cc] = NaN\n",
    "                diOut2[pr][rr,cc] = NaN\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.62, 0.04, 'Search intensity, $\\\\rho$')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Figure 8\n",
    "\n",
    "## set up canvas\n",
    "fig = PyPlot.figure(figsize=(5,5), facecolor=\"w\", dpi=100) # create figure\n",
    "fig.subplots_adjust(left=.17, right=.97, bottom=0.15, top=.95) # reduce white spaces\n",
    "ax = fig.add_subplot(111) # create axis\n",
    "\n",
    "## plot\n",
    "ax.plot(ρRange, log.(diOut2[:mLO][:,1] ./ diOut1[:mLO][:,1])*1e4) # bps\n",
    "ax.axhline(0.0, ls=\":\", color=\"gray\")\n",
    "\n",
    "## format axes\n",
    "ax.spines[\"right\"].set_visible(false)\n",
    "ax.spines[\"top\"].set_visible(false)\n",
    "arrowed_spines(ax) # add arrows\n",
    "ax.set_xlim([1,1e3])\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_ylim([-2.0,15])\n",
    "ax.set_yticks(0:3:15)\n",
    "\n",
    "## label axis next to arrows\n",
    "ax.annotate(L\"\\shortstack[l]{Relative change in $m_{lo}$ (in basis points)\\\\when $n$ increases from 27 to 28}\", xy=(0.03,0.94,), xycoords=\"axes fraction\") # left y label\n",
    "ax.annotate(L\"Search intensity, $\\rho$\", xy=(0.62,0.04), xycoords=\"axes fraction\") # x-axis label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(30.26811417362842, 0.5, 'Search intensity, $\\\\rho$')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Figure 9\n",
    "\n",
    "## specify parameters for plotting\n",
    "prSymbol = :welfare\n",
    "liLevels = [0.0,] # contour levels\n",
    "\n",
    "## set up canvas\n",
    "fig = PyPlot.figure(figsize=(5,5), facecolor=\"w\", dpi=100) # create figure\n",
    "fig.subplots_adjust(left=.15, right=.95, bottom=0.15, top=.95) # reduce white spaces\n",
    "ax = fig.add_subplot(111) # create axis\n",
    "\n",
    "## calculation\n",
    "ydSelection = findfirst(ydRange .>= 0.898):length(ydRange)\n",
    "aPlot = log.(diOut2[prSymbol] ./ diOut1[prSymbol])[:,ydSelection]*1e4\n",
    "xvalues = ydRange[ydSelection]\n",
    "yvalues = [isnothing(findfirst(aPlot[:,j].>=0.0)) ? maximum(ρRange)*1.01 : ρRange[findfirst(aPlot[:,j].>=0.0)] for j in 1:length(xvalues)]\n",
    "\n",
    "## plot\n",
    "ax.plot(xvalues, yvalues, lw=1.5, ls=\"--\", c=\"k\")\n",
    "ax.fill_between(xvalues,minimum(ρRange)*ones(length(yvalues)),yvalues)\n",
    "ax[:annotate](L\"$\\Delta{w}>0.0$\",\n",
    "    xycoords=\"data\", xy=[.93,1e2], rotation=0, color=\"k\",\n",
    "    bbox=Dict(:boxstyle=>\"square,pad=0.1\", :fc=>\"white\", :ec=>\"None\", :lw=>0), zorder=1000)\n",
    "ax[:annotate](L\"$\\Delta{w}<0.0$\",\n",
    "    xycoords=\"data\", xy=[1.03,1e1], rotation=0, color=\"k\",\n",
    "    bbox=Dict(:boxstyle=>\"square,pad=0.1\", :fc=>\"None\", :ec=>\"None\", :lw=>0), zorder=1000)\n",
    "\n",
    "## set axes\n",
    "ax.set_ylim([1e0,1e3])\n",
    "ax.set_xlim([0.9,1.10])\n",
    "ax.set_xticks(0.9:0.05:1.10)\n",
    "ax.set_xticklabels([\"0.90\",\"0.95\",\"1.0\",\"1.05\",\"1.10\"])\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(L\"(Relative) dealer flow utility, $\\hat{y}_d$\")\n",
    "ax.set_ylabel(L\"Search intensity, $\\rho$\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.6.5",
   "language": "julia",
   "name": "julia-1.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
